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View mapSpeaker: Guillaume Remy (IAS, Princeton)
Title: Modular transformation of conformal blocks via Liouville CFT.
Abstract: Conformal blocks are objects of fundamental importance in mathematical physics. They are a key input to the conformal bootstrap program to exactly solve 2D conformal field theory (CFT) and are related to 4D supersymmetric gauge theory through the Alday-Gaiotto-Tachikawa correspondence. They are typically defined as power series via the representation theory of the Virasoro algebra but in this talk we will provide novel probabilistic expressions using the Gaussian free field. This will allow us to obtain many analytic properties such as modular transformations. Our methods are based on recent developments in the probabilistic construction of the Liouville CFT, a theory first introduced to describe random surfaces by A. Polyakov in the context of string theory. Based on joint work with Promit Ghosal, Xin Sun, and Yi Sun.
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